Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties

Abstract

We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension $n\ge 4$ determined by general position properties, the piecewise disjoint arc-disk property is satisfied.

References in corpus (3)

• Path concordances as detectors of codimension-one manifold factors
• Detecting codimension one manifold factors with topographical techniques
• Survey on the Generalized R. L. Moore Problem